Title:

Polarimetric modelling for anisotropic stars

A theoretical description of the polarization of light, generated by an anisotropic point light source and scattered by an arbitrary shape envelope, is developed in this work, the mechanism of scattering being assumed to be either Thomson or Rayleigh scattering. The description is a development of the earlier work of J. F. L. Simmons' (1982) where he expressed the scattering function and scatterer density distribution function as a summation of multipole contributions. Whereas Simmons analysis was based on an isotropic point light source, the present analysis permits a variable flux to represent the anisotropy of the light source. Thomson or Rayleigh scattering is assumed throughout, and in all cases the scattering envelope is taken to be large compared to the light source. This allows the anisotropy to be expressed in terms of projected area. The model has applicability to rotating, pulsating, binary, and active stars with hot extended envelopes. The thesis is divided into five chapters plus four appendices. Following a review of previous work in Chapter One, together with a discussion of the motivation and interest of stellar polarimetry, in Chapter Two the theoretical analysis is established for scattering polarization with an anisotropic point light source within a spherical envelope. This analysis is then applied to an ellipsoidal black body star within a spherical envelope, for which we get explicit integral expressions for the Stokes' parameters and an analytical solution for the special case of a star with a circular equator. As examples of ellipsoidal stars the polarization from a single distorted star (due to e. g. the rotation) such as Be stars, Xray binaries filling its Roche lobe (e. g. Cygnus X1 and Centaurus X3) , and pulsating stars (pulsating as a series of ellipsoids) is calculated. The latter show a very complicated pattern of quloci, which, in principle, fit the polarization behaviour of such types as RV Tau and Omicron Ceti. The maximum polarization of about 20% of the total light is expected from a disk like light source viewed edge on (Galaxies would be good example, since they are very distorted light sources). In Chapter Three the anisotropic light source theory is generalized to include an arbitrarily shaped envelope. In the harmonic summation which results it is found that approximation up to the second order terms is quite acceptable, when both the light source and the envelope are ellipsoidal. The maximum polarization is enhanced (due to the envelope being ellipsoidal) to about 35% when a disk of scatterers is perpendicular to the disk like star observed edge on. In general whether the polarization undergoes enhancement or cancellation is dependent on the angle between the rotation axis of the ellipsoidal star and the axis of symmetry of the ellipsoidal envelope. The effects of rotation and pulsation are also calculated. In Chapter Four the analysis is applied to the case of light source anisotropy arising from a nonuniform photosphere (e. g. hot or cool spot). Calculation of the projected area of the spot as it varies during stellar rotation is done without any of the simplifying assumptions usually made in stellar light curve modelling. Again the approximation of the second order terms of the harmonic summation is acceptable for spots of likely physical size (e.g. of angular extent < 30°).
